IL144914A

IL144914A - Device for hybridizing a satellite positioning receiver with an inertial unit

Info

Publication number: IL144914A
Application number: IL144914A
Authority: IL
Original assignee: Thales Avionics Sa
Priority date: 1999-12-21
Filing date: 2001-08-15
Publication date: 2006-06-11
Also published as: EP1157284A1; FR2802732B1; IL144914A0; FR2802732A1; ZA200106724B; WO2001046712A1

Description

Device for hybridizing a satellite positioning receiver with an inertial unit Thales Avionics S.A.

C. 134949 DEVICE FOR THE HYBRIDIZATION OF A SATELLITE-BASED POSITIONING RECEIVER WITH AN INERTIAL RIG The present invention relates to the hybridization with the aid of a Kalman filter, of the information delivered by a satellite-based positioning receiver with the information originating from an inertial rig.

Kalman filtering, which appeared in 1960, is a signal processing technique making it possible to reduce, in an optimal manner, noise from various origins, inevitably accompanying the signals produced by an item of equipment, by modelling the changes in the state of the relevant item of equipment within its environment and by modelling the dependency relation existing between the measurable signals originating from the item of equipment and its state. It deploys a recursive filter whose implementation is greatly facilitated by the generalization of digital signal processing operations. Its field of application is very broad since it applies to any system in which the changes in its state and the dependency relation between its state and signals accessible to measurement can be modelled. It is widely used in aeronautics, for the processing of noise impairing periodically renewed measurements and for the merging of information of the same type emanating from measurements originating from several items of equipment employing different physical principles .

An important field of use of Kalman filters is that of navigation computers which have to calculate flight-assistance information such as position, attitudes (roll, pitch and heading) and velocity vector with the best possible accuracy, despite the measurement noise and defects inherent in each sensor. Within the context of navigation computers, the Kalman filter enables short-term predictions to be made about the errors impairing the expected inertial data (position, attitudes and velocity vector) from the estimates of the values taken by the same errors in the recent past and from their known laws of change as a function of the environment of the flight computer, and makes it possible to deduce from these short-term forecasts, corrections to be made to the information derived from the measurements originating from the sensors, so as to render them optimal, that is to say as accurate as possible .

The technique of Kalman filtering will not be detailed here since it is within the competence of the person skilled in the art and has already formed the subject of a great deal of literature.

In short, the Kalman filtering technique is based on the possibility of modelling the changes in the state of a relevant physical system within its environment, by means of a so-called "equation of change", and on the possibility of modelling the dependency relation existing between the state of the relevant physical system and the signals or "measurement" by which it is perceived from outside, by means of a so-called "observation equation" so as to make an a-priori forecast of the state of the system and of the measurement, given the history.

It consists in subjecting the actual measurement referred to by the term "measurement vector" since it often entails several quantities, to a filtering making it possible to extract therefrom an a-posteriori estimate of the state of the system also referred to as the "state vector" since the state of a system is often defined using several items of information not necessarily equal in number to that of the measurement quantities, which is optimal, in the sense that it minimizes the covariance of the error made in this a-posteriori estimation of the state of the system. The filter used to do this is a recursive adaptive filter which generates a-priori estimates of the state vector of the system and of the measurement vector from the equation of change and from the observation equation, and which uses the deviation noted between the measurement vector actually noted and its a-priori estimate to produce a corrective term which, applied to the a-priori estimate of the state vector of the system, leads to the obtaining of the a-posteriori optimal estimate.

The adaptive adjustment of the Kalman filter is achieved with the aid of a servocontrol loop tending to minimize the covariance of the error made with regard to the a-posteriori estimation of the state vector of the system. The equations defining the Kalman filter which are well known, will be recalled later.

One of the oldest applications of the Kalman technique, in aeronautics, relates to the correction of the errors impairing the position, attitude and velocity vector information obtained by a navigation computer on the basis solely of the information delivered by the sensors of an inertial measurement unit, an operation referred to as "the hybridization of an inertial rig" .

In this application, the Kalman filter is used to supply an optimal estimation of the errors impairing the information extracted from the measurements delivered by the inertial rig by the navigation computer. The system, whose dynamic behaviour is modelled, has as state vector, a vector having as components the errors in the information made by the computer from the measurements of the inertial rig and as measurement vector a vector having as components, measured errors in information accessible to measurement. The modelling of its dynamic behaviour is defined by means of an equation of change reflecting, as faithfully as possible, the deterministic laws known to be followed by the relevant errors in the environment in which the system is immersed, dependent for example on the kinematics of the motion of the carrier of the inertial rig, and by an observation equation reflecting the dependency relations existing between the errors in the information accessible to measurement and the errors taken into account in the state vector. In a case where the deterministic change in an error relating to an item of information is not known, it is regarded as static when defining the equation of change. In practice, the measurement vector, which does not necessarily have the same dimension as the state vector, consists of the deviations noted between two versions of one and the same item of information which are deduced the one from the signals of the inertial rig and the other from the signals of the one or more other items of equipment not subject to the same drift. This item of information can be, for example, the heading deduced on the one hand from the measurements of the sensors of the inertial rig, and on the other, from the measurement of a compass or a radio compass, the altitude deduced on the one hand from the measurements of the sensors of the inertial rig, and on the other, from the measurements of a radio altimeter or barometric altimeter, the velocity or the relative position of the craft with respect to a ground reference on the one hand delivered by a radar, and on the other reconstructed from the measurements of the inertial rig, or else the position and the velocity vector on the one hand delivered by a satellite-based positioning receiver or GNSS (Global Navigation Satellite System) receiver, and on the other extracted from the measurements of the inertial rig.

In a first step, the navigation computer performs the conventional computations, by integrations, making it possible to obtain information about the position, the attitudes and the velocity vector of its carrier from the raw data supplied by the sensors of the inertial measurement unit, whereas in a second step, a Kalman filter performs optimal estimations of the errors made, used to correct or readjust, in a third step, the information delivered by the navigation computer.

By applying the Kalman filtering to the estimation of the errors impairing the physical quantities measured and not to the estimation of the physical quantities themselves, the Kalman filter is enabled to operate on a less changeable signal of lower amplitude, the modelling of whose dynamic behaviour lends itself better to a linear approximation.

Another known application of the Kalman filter relates to the filtering of measurement noise in the processing part of a GNSS receiver.

A GNSS receiver is composed of a reception part which supplies, for each satellite of the constellation of the positioning system whose transmission signals are picked up, the data transmitted by this satellite and two sorts of measurements, namely the pseudo-distance and pseudo-velocity of the receiver with respect to the relevant satellite, and of a computation part which from these data and measurements, supplies the position and the velocity vector of the carrier of the receiver as well as the time. The computation part operates on the basis of the data transmitted by the visible satellites and of the measurements of the reception part .

The system which the computation part has to solve in order to obtain the position (or the velocity) has four unknowns (position x, y, z and time t or velocity Vx, Vy, Vz and clock drift) and comprises as many equations as visible satellites. A GNSS receiver is therefore capable of delivering a measurement of position and of velocity vector of its carrier, as well as of time, as soon as it picks up four satellites of the positioning system. In practice, it often picks up more than four. The number of equations then being greater than the number of unknowns, the solution can be obtained by the method of least squares, which makes it possible to minimize the variance of the errors in the position and the velocity solved for, which are due to the measurement noise. In this case the accuracy in the solved position and solved velocity depends only on the geometry of the constellation of the visible satellites, which is characterized by the DOP parameter (Dilution Of Precision) . This technique is a particular case of the Kalman filter, with no memory effect, since a reliable model of the dynamics of the carrier is often lacking, at the GNSS receiver level, for producing a true Kalman filter.

In the presence of a GNSS receiver and of an inertial rig, it has quite naturally been sought to use the technique of Kalman filtering to merge their navigation information at the level of the navigation computer of the inertial rig. Such an operation is known in the art by the name of "hybridization between a GNSS receiver and an inertial reference" .

Two sorts of hybridizations between a GNSS receiver and an inertial reference are known: so-called "loose hybridization" and so-called "tight hybridization" .

Loose hybridization consists in using, with a navigation computer equipped with an inertial measurement unit, a complete GNSS receiver, with its special-purpose computer often provided at output with a first Kalman filter customarily degenerated into a least squares filter, with no memory effect and in furnishing the navigation computer with an error estimator, in the form of a second Kalman filter based on the modelling of the dynamic behaviour of a physical system consisting of the inertial measurement unit, the navigation computer and the part of the GNSS receiver delivering the clock signal.

The modelled system used for the design of this second Kalman filter has, among the components of its state vector, the expected errors in the position coordinates of the craft carrying the navigation computer and the GNSS receiver and the expected errors in the components of the velocity vector of the craft, which are derived from the acceleration components and angular velocities delivered by the navigation computer .

The measurement vector adopted for operating this second Kalman filter has, among the components of its measurement vector, the deviations between two versions of the position co-ordinates and of the components of the velocity vector, the one delivered by the GNSS receiver, the other delivered by the inertial navigation computer.

The adopted modelling of the dynamic behaviour of the system is defined, in the customary manner, by an equation of change reflecting the known deterministic laws of change for the components of its state vector and by an observation equation reflecting the dependency relations existing between the measurement vector and the state vector.

This loose hybridization has various drawbacks.

Firstly, it requires, on the part of the GNSS receiver, the delivery of a complete measurement of position and of velocity vector and cannot operate if the GNSS receiver picks up only an insufficient number of satellites of the positioning system (fewer than four) .

It does not make it possible to take account of the quality of the information delivered by the GNSS receiver, which is related to the geometry of the constellation of the visible satellites (Dilution Of Precision) .

On the other hand, it can be used in all circumstances, without particular precaution, since it does not call upon, on the part of the GNSS receiver, any-confidential data such as the measurements of corrected pseudo-distances of the intentional scrambling intended to reduce the accuracy of the positioning for users not agreed by the manager of the satellite-based positioning system. This problem of making the GNSS system secure arises, however, within the GNSS receiver itself but it can be solved through particular arrangements ensuring the confinement of the confidential data in a restricted protected volume.

Tight hybridization between a GNSS receiver and an inertial reference consists in operating at the level of the basic information available in a GNSS receiver, namely the pseudo-distances or relative distances separating the GNSS receiver from the satellites received and the pseudo-velocities or velocities of the relative displacements of the satellites received with respect to the GNSS receiver, and hence in short-circuiting, in respect of the readjusting of the navigation computer, the computation part of the receiver.

The Kalman filter used at the level of the navigation computer is then based on the modelling of the dynamic behaviour of a system defined by: a state vector with, among its components, the expected errors in the position co-ordinates and in the components of the velocity vector, which are extracted from the acceleration components and from angular velocities delivered by the navigation computer, and the bias and the drift of the clock of the receiver, an equation of change reflecting the known laws of change of the components of its state vector, a measurement vector with, among its components, deviations between two versions of pseudo- distances and of pseudo-velocities having as origin the one the satellite-based positioning receiver and the other the navigation computer, an observation equation reflecting the dependency relations existing between the measurement vector and the state vector.

The navigation computer performs the processing operations required to extract the information regarding position, velocity vector and attitudes of the carrier from the measurements of the inertial measurement unit. It then calls upon this information relating to the position and velocity vector of the carrier as well as upon the information about the positions and velocity vectors of the satellites of the positioning system supplied to it by the GNSS receiver on the basis of the data transmitted by the satellites themselves to calculate the values of the pseudo-distances and pseudo-velocities between the carrier and these satellites.

We are then in possession of two versions of the pseudo-distances and pseudo-velocities, one derived from the measurements of the inertial measurement unit and from the data transmitted by the satellites, the other derived from the measurements of the GNSS receiver relating to the durations of transmission and the Doppler shifts affecting the signals transmitted by the visible satellites of the positioning system.

The deviations between these two versions, constituting the measurement vector, are then subjected to a Kalman filtering so as to filter the measurement noise and obtain an a-posteriori optimal estimate of the state vector utilized to readjust the navigation computer.

The most apparent advantage of this form of tight hybridization is of avoiding having to involve the computation part of the GNSS receiver and of using a single Kalman filter rather than two nested filters, one processing the output signals from the computation part of the GNSS receiver and the other the drift of the navigation computer.

The other advantage, which is important from the point of view of accuracy, is the fact that the geometry of the satellites (number and arrangement in space) is taken into account through the possibility of readjusting the a-priori estimate of the position and of the velocity vector which are deduced from the measurements of the inertial rig in the various directions of the satellites received, regardless of their number.

Tight hybridization, as currently practised, has the drawback on the other hand of requiring the extraction, from within the GNSS receiver, of the measurements of pseudo-distances, pseudo-velocities of the satellites of the positioning system, these being items of information which are sensitive once they are corrected of the effects of intentional scrambling. This compels us to place the GNSS receiver and the navigation computer within one and the same security cordon, thereby posing severe problems with the arrangement of the equipment on a carrier and raising the cost of their installations.

The aim of the present invention is to avoid the aforesaid drawbacks.

Its subject is a device for the hybridization, within a navigation computer, of a satellite-based positioning receiver with an inertial rig equipping a craft, comprising a Kalman filter, with an input and an output, based on the modelling of the dynamic behaviour of a system and defined by: a state vector with, among its components, the expected errors in the position co-ordinates and in the components of the velocity vector, which are extracted from the acceleration components and from angular velocities delivered by the navigation computer, an equation of change reflecting the known laws of change of the components of its state vector, a measurement vector with, among its components, deviations between two versions of pseudo-distances and of pseudo-velocities having as origin the one the satellite-based positioning receiver and the other the navigation computer, an observation equation reflecting the dependency relations existing between the measurement vector and the state vector, characterized in that it comprises, interposed in front of the input of the Kalman filter, a synthesis circuit for synthesizing the deviations between pseudo-distances and pseudo-velocities operating on the basis of the two versions of the craft's position and velocity vector information delivered, the one by the satellite-based positioning receiver and the other by the navigation computer and using, to do this, the direction cosines of the axes joining the craft to the visible satellites of the positioning system as deduced from the positions of the said visible satellites as extracted from the data transmitted by them and picked up by the satellite-based positioning receiver, and from one of the available versions of the craft's position information.

Advantageously, the Kalman filter has, among the components of its state vector, the bias and the drift of the clock of the receiver.

Advantageously, the synthesis circuit deduces the direction cosines of the axes joining the craft to the visible satellites of the positioning system, from the positions of the said visible satellites as extracted from the data transmitted by them and picked up by the satellite-based positioning receiver, and from the version of the craft's position information delivered by the navigation computer.

As a variant, the synthesis circuit deduces the direction cosines of the axes joining the craft to the visible satellites of the positioning system, from the positions of the said visible satellites as extracted from the data transmitted by them and picked up by the satellite-based positioning receiver, and from the version of the craft's position information delivered by the satellite-based positioning receiver.

As a variant, the synthesis circuit receives the values of the direction cosines of the axes joining the craft to the visible satellites of the positioning system directly from the satellite-based positioning receiver which itself deduces them from the positions of the said visible satellites as extracted from the data transmitted by them and from its own version of information regarding the position of the craft as delivered by the navigation computer.

Mixed hybridization is thus obtained, having the same advantages from the point of view of a least squares criterion (optimality) as tight hybridization, whilst not calling upon sensitive data or those not necessarily accessible from the reception part of the GNSS receiver.

Other characteristics and advantages of the invention will emerge from the following description of an embodiment of the invention, given by way of example.

This description will be given in conjunction with the drawing in which: Figure 1 represents the schematic diagram of a Kalman filter, - Figure 2 represents the schematic diagram of a "loose" hybridization between an inertial rig and a GNSS receiver according to the state of the prior art, Figure 3 represents the schematic diagram of a "tight" hybridization between an inertial rig and a GNSS receiver according to the state of the prior art, and Figure 4 represents the schematic diagram of a hybridization according to the invention.

In Figure 1, the quantities relating to the measurement or to the state of a system as a function of the fact that this involves a measurement or an actual state or that this involves a measurement estimation or state estimation are distinguished by endowing or otherwise the terms which represent them with a circumflex accent and with a double subscript. Thus, the actual measurement applied to the input of the Kalman filter shown in Figure 1 is denoted zi whilst the optimal estimate of the state of the system available at the output of this Kalman filter is denoted x iH or Xi/ι.χ. The subscript i/i signifies that this pertains to an a-posteriori estimation regarding step i from information available in step i whereas a double subscript i/i-1 signifies that this pertains to an a-priori forecast regarding step i from information originating from step i-1.

A Kalman filter makes it possible to obtain an estimation of the a-posteriori state of a system, optimal in the sense that the covariance of the error made in this a-posteriori estimation is minimal. It is based on modelling the changes in the system and on modelling the relation existing between the measurement and the state of the system.

In its greatest generality, the modelling of the changes in the state of the system is defined by a vector differential equation of first order which is expressed, after discretizing the continuous model, by an equation of change of the form: xi+1. Ρ, , + I,,!!* + Wj x being a state vector of dimension n, u a control vector, FA a matrix defining the relation between the state vector at step i and the state vector at step i+1 in the absence of any control vector and any operating noise, Li a matrix defining the relation between the control vector and the state vector during one and the same step and w operational noise during a step, assumed to be white and Gaussian with zero mean value.

The modelling of the relation existing between the measurement and the state of the system is defined by another first-order differential equation which is expressed, after discretizing the continuous model, by an observation equation of the form: *i = + z being a measurement vector of dimension m, H± a matrix defining the relation between the measurement vector and the state vector during one and the same step and v measurement noise during a step, which is assumed to be white and Gaussian with zero mean value.

As represented in Figure 1, the alman filter is recursive. It relies on the determination of an a-priori estimation of the state vector of the system at step i from a-posteriori knowledge of the state vector of the system i^/^ at the previous step i-1 and from the application to this a-priori estimate x i/i-i °f a corrector term depending on the deviation noted between the measurement vector z± noted during this step i and its a-priori estimate z^.j deduced from the a-priori estimation of the state vector.

The a-priori estimate of the measurement vector at step i is determined by applying the equation of change and observation equation to the a-posteriori estimate Xi-i/i-i °f tne state vector and to the control vector corresponding to the previous step i-1. This operation is illustrated in Figure 1 by the presence of a feedback loop consisting of a delay circuit 1, three filters 2, 3, 4 and a summator 5.

The delay circuit 1 connected at the output of the Kalman filter makes it possible to store the a-posteriori estimate x i-i/i-i of the state vector available at the output of the Kalman filter during the previous step i-1.

The two filters 2 and 3 and the summator 5 make it possible, by implementing the observation equation, to obtain the a-priori estimate x i/ι.χ of the state vector at step i, from the a-posteriori estimate J.^.J of the state vector of the system at the previous step i-1.

The filter 2 supplies the component of the a-priori estimate x of the state vector at step i dependent on the a-posteriori estimate of the state vector at step i-1. Its transfer function is defined by the matrix Ρ±. of the observation equation.

The filter 3 supplies the component of the a-priori estimate £i i-a of the state vector at step i dependent on the control vector corresponding to step i-1.

Its transfer function is defined by the matrix of the observation equation.

The summator 5 adds together the two components delivered by the filters 2 and 3 and supplies the a-priori estimate i^.j of the state vector at step i such as it results from the application of the equation of change.

This a-priori estimate i^.j of the state vector at step i is then used to obtain, by means of a third filter 4, the a-priori estimate z of the measurement vector at step i by applying the equation of change. This third filter 4 has, to do this, a transfer function defined by the matrix i¾ of the observation equation.

The a-priori estimate z^.j of the measurement vector at step i obtained in the feedback loop is applied, at the input of the Kalman filter, to a subtractor circuit 8 which also receives the measurement vector actually measured during step i, z± which delivers an error vector x± attesting to the error made during the a-priori estimation. This error vector r± is transformed by a fourth filter 6 into a correction vector. This correction vector is added by a second summator 7 to the a-priori estimate x of the state vector for step i emanating from the first summator 5, to obtain the a-posteriori estimate x i of the state vector which constitutes the output of the Kalman filter.

The fourth filter 6, which supplies the corrective term, is known as the readjustment gain filter. It has a transfer function defined by a matrix Kt determined in such a way as to minimize the covariance of the error made in the a-posteriori estimation.

Kalman has shown that the matrix of optimal gain Ki could be determined by a recursive method from the equations : for the covariance matrix of the a-priori estimate of the state vector P - F P FT +0 for defining the gain matrix itself - for updating the covariance matrix of the a-posteriori estimate of the state vector P„, =(l-KlHi)P„,_i P being the covariance matrix of the state vector, either estimated a-priori for step i on the basis of step i-1 if P is indexed with the subscript i/i-1, or estimated a-posteriori if P is indexed with the subscript i-1, R being the covariance matrix of the observation noise Q being the covariance matrix of the state noise vt.

On initialization, the covariance matrix of the state vector and the state vector are taken equal to their most likely estimates. At worst, the covariance matrix is a diagonal matrix with infinite or very large terms (so as to have very large standard deviations as compared with the domain within which the changes in the state vector may occur) and the estimate of the state vector, the zero vector, when we have no idea as to the initial values.

In practice, the correction gain of a Kalman filter is "proportional" to the uncertainty in the a-priori estimation of the state of the system and "inversely proportional" to the uncertainty in the measurement.

If the measurement is very uncertain and the estimation of the state of the system relatively accurate, the deviation noted is due mainly to measurement noise and the correction stemming therefrom must be small. Conversely, if the uncertainty in the measurement is small and that in the estimation of the state of the system large, the deviation noted is very representative of the estimation error and must lead to a large correction. This is the behaviour to which we tend with the Kalman filter.

To summarize, the construction of a Kalman filter requires the definition of two matrices F and L corresponding to the equation of change defining the changes in the state vector of the physical system modelled, of a matrix H corresponding to the observation equation defining the relations making it possible to go from the measurement vector to the state vector and of the gain matrix K updated with the aid of an iterative procedure involving the covariance matrix of the state vector P itself updated during the iterative procedure and of the covariance matrices Q and R of the state noise and observation noise.

It is pointed out, this will have its usefulness subsequently, that if we no longer wish to take into account the state vector of the system at the prior step and hence to eliminate the memory effect of a Kalman filter, it is sufficient therefor to replace at each step Pf/M = F^P^ ^F^i + Qt_ by a diagonal matrix pi/i-i with infinite or very large terms (so as to have very large standard deviations as compared with the domain within which the changes in the state vector may occur) Xi/i-\Xi · In this case the matrices F and Q become unnecessary and the a-posteriori estimate xt/i of the state vector becomes independent of the a-priori estimate of the state vector, which can be taken equal to zero.

The technique of Kalman filtering is often used when needing to search for an optimal estimation of one and the same physical quantity, several estimates of which are available from several items of equipment operating according to different physical principles and not exhibiting the same defects.

In the case of hybridization between an inertial rig and a GNSS satellite-based positioning receiver, the Kalman filtering is performed at the level of the deviations noted between two versions of the information of the same type originating the one from the inertial rig and, the other from the GNSS receiver, since this makes it possible to work on variables having more restricted domains of variation over which the linear approximation can be used to simplify the modelling equation and the equation of change.

In this use of the Kalman filtering, the equation of change modelling the forecastable changes in the errors made by the navigation computer with regard to the information which it deduces from the measurements supplied by the inertial measurement unit is in fact reflected by a single matrix F which depends on the parameters of the motion of the carrier, that is to say on the flight parameters in the case where the carrier equipped with the navigation computer and with the inertial measurement unit is an aircraft. The definition of the various versions of this matrix F as a function of the parameters of the motion of the carrier is outside the field of the present invention. It will not be detailed hereinbelow since it is well known to the person skilled in the art specializing in the field of inertia.

Figure 2 represents the schematic diagram of a loose hybridization between an inertial rig and a GNSS receiver. Seen therein are: the inertial measurement unit I U 10 which delivers increments of angles ΔφχίΔφ1,ίΔφ!! and increments of velocity Δνχ, Δνγ, Δνζ in a trihedral of orientation x, y, z tied to its sensors, - the navigation computer 11 which receives the increments of angles and of velocities emanating from the IMU 10 and extracts therefrom the position P, the velocity vector V and the attitudes Att of the carrier and - the GNSS receiver 13 which supplies another version of the position P and of the velocity vector V.

To facilitate comparison with the following setups, the GNSS receiver 13 is depicted in a representation detailing its reception part 13a delivering the pseudo-distances pd and pseudo-velocities pv of the carrier with respect to the visible satellites, and its computer part 13b extracting from pseudo-distance information pd and pseudo-velocity information pv, the position P and the velocity vector V of the carrier.

In this loose hybridization, position and velocity vector originating from the navigation computer 11 and from the GNSS receiver 13 are subjected to a subtractor 14 determining their deviations. The deviations noted in position ΔΡ and velocity vector Δν feed a Kalman filter 15 which extracts therefrom an a-posteriori optimal estimation of the measurement biases of the sensors of the inertial measurement unit IMU 10 and of the errors made in the position P, the velocity vector V and the attitudes of the carrier by the navigation computer, and which applies this a-posteriori optimal estimation to the navigation computer so as to readjust it.

The Kalman filter 15 used here is based on an equation of change corresponding to a modelling of the drifting of the system consisting of the navigation computer 11 fed with information by the inertial measurement unit 10 and on an observation equation modelling the relations existing between the measurement vector and the state vector.

The computer 13b of the GNSS receiver 13 generally uses a Kalman filter often reduced to a memoryless least squares filter which performes spatial filtering with a view to extracting, from the pseudo-distance information pd and pseudo-velocity information pv, a single item of information pertaining to the position and velocity vector of the carrier and to the time which is as accurate as possible while reducing the measurement noise of the GNSS receiver. This results in a complex structure with two nested Kalman filters.

Independently of this, loose hybridization also has the drawback of demanding, in order to be operational, a complete measurement on the part of the GNSS receiver 13 which must therefore have been able to pick up at least the signals from four satellites of the positioning system.

Figure 3 represents the schematic diagram of a tight hybridization between an inertial rig and a GNSS receiver.

As before, the IMU 10 delivers increments of angles ΔφχίΔφγ,Δφζ and increments of velocity Δνχ, Δνγ, Δνζ in a trihedral of orientation x, y, z tied to its sensors, to a navigation computer 11 responsible for extracting from these increments of angles and velocity, the position P, the velocity vector V and the attitudes Att of the carrier, whilst the GNSS receiver 13 supplies another version of the position P and of the velocity vector V of the carrier.

Here, the GNSS receiver 13 is used to readjust the navigation computer 11 in a different manner from loose hybridization. The final items of information regarding the position P and the velocity vector V of the carrier which are delivered by its computer 13b, are not employed for readjustment. They are replaced by the intermediate measurements of pseudo-distances pd and of pseudo-velocities pv with respect to the various visible satellites of the constellation of the positioning system which are available at the output of its reception part 13a.

To do this, a synthesizer circuit S 20 is appended at the output of the navigation computer 11. It receives from the GNSS receiver, via a particular link, complementary items of information regarding the positions and velocities of the satellites as extracted from the data transmitted by the satellites themselves and computes, from these complementary items of information and from the carrier position P and velocity V information delivered by the navigation computer 11, estimations pd and pv of the pseudo-distances and pseudo-velocities. The two versions of pseudo-distances pd and pseudo-velocities pv available, the one computed by the synthesizer S 20 and the other measured by the reception part 13a of the GNSS receiver 13 are subjected to a deviation detector 21. The deviations noted Apd and Δρν between the two versions of each pseudo-distance and of each pseudo-velocity are applied as input to a Kalman filter 22 which delivers, as output, an a-posteriori optimal estimate of the measurement biases of the sensors of the inertial measurement unit IMU 10 and of the errors made in the position P, the velocity vector V and the attitudes of the carrier by the navigation computer. This a-posteriori optimal estimation is then subjected to the navigation computer so as to readust it.

The Kalman filter 22 used here can be based on the same equation of change as the Kalman filter 15 used previously for the loose harmonization illustrated in Figure 2. On the other hand its observation equation must be tailored to the new measurement vector.

In a general manner, the estimated state vector X of the Kalman filters used in the loose or tight harmonization devices of Figures 2 and 3 is of dimension n and contains various components, including: Syxf SyytSyg belng the errors in the componets vx, vy, vz of the velocity of the carrier, t being the bias of the clock of the GNSS receiver, d being the drift of the clock of the GNSS receiver, Sx, Sy, S2 being the errors in the co-ordinates x,y,z of the position of the carrier, and there is associated, with the estimated state vector X, a square covariance matrix P of dimension n x n.

The Kalman filtering consists in optimally readjusting the state vector estimated from the measurement vector Z by making the following correction to it: δΧ = KZ K being the gain matrix whose method of determination described in relation to Figure 1 calls upon the state vector covariance matrix P updated according to an iterative procedure, upon the covariance matrix R of the observation noise, upon the observation matrix H and upon the measurement vector or observation vector Z.

Since the covariance matrix P of the state vector is updated iteratively starting at worst from an initial covariance matrix exhibiting an infinite standard deviation, the Kalman filter is fully defined by means of its estimated state vector X, of the matrix F defining by modelling, the changes in its state vector, of its observation vector Z, of the matrix H defining the relations between observation vector and state vector, and of the covariance matrix R of the observation noise.

Within the context of the loose hybridization of Figure 2, the elements to be taken into consideration when defining the Kalman filter, apart from the matrix F reflecting the equation of change of the model are: for the part relating to the position readjustment : XGNSS rx 0 0 z= yGNSS R = 0 y ZGNSS 0 0 3x3 position estimated by the navigation computer in the terrestrial reference frame XGNSS yGNSS position estimated by the GPS receiver in the ZGNSS J terrestrial reference frame yWSsi and for the velocity readjustment part vx ~ vxGNSS 'rvx 0 0 z = vy - vyGNSS R = 0 0 vz ~vzGNSS 0 0 rvz velocity vector in the terrestrial reference frame delivered by the navigation computer vxGNSS vyGNSS velocity vector in the terrestrial reference vzGNSS . frame delivered by the GPS receiver associated with the velocity vector measured by the GPS receiver In the computer part of the GNSS receiver, another Kalman filter often reduced to a least squares filter, that is to say a memoryless filter, is used to solve for the position, the velocity vector of the carrier and the time whilst minimizing the measurement noise. The elements to be taken into consideration in defining it are : for the part relating to the position readjustment : δχ/δν,δζ being the deviations between the actual position of the carrier and an a-priori estimate of this position, t being the error made in the time by the clock of the GNSS receiver, which error is rendered akin to a distance by multiplying by the velocity of light, being the direction cosines of the axis joining the carrier to the i-th satellite in the reference frame used by the navigation computer, x,y,z being the a-priori estimate of the position of the carrier, as given by the GNSS receiver before correction, and deduced for example from the position estimated at the previous solution, xifYi/ zi being the position of the i-th satellite of the positioning system as extracted from the data of the i-th satellite, and expressed in the same reference frame as the position of the carrier, Pi being the a-priori psuedo-distance separating the carrier from the i-th satellite, as computed from the a-priori position of the carrier and from the data transmitted by the i-th satellite, pdi being the pseudo-distance between the carrier and the i-th satellite as measured by the GNSS receiver, and rpdi the variance of the pseudo-distance measured pd± . for the part relating to the velocity: dpi = (vx - + (v - )# +(v, - vjr, δνχ,δνγ,δνζ being the components of the deviation between the actual velocity vector of the carrier and an a-priori estimate of this velocity vector, d being the drift of the clock of the GNSS receiver, which drift is rendered akin to a velocity by multiplying by the velocity of light, vx,vy,vz being the a-priori estimate of the components of the velocity vector of the carrier, as given by the GNSS receiver before correction, and deduced for example from the velocity vector estimated at the previous solution, vxi,vyi,v2i being the components of the velocity vector of the i-th satellite of the positioning system extracted from the data of the i-th satellite itself, as expressed in the reference frame used for the velocity vector of the carrier, dpi being the pseudo-velocity between the carrier and the i-th satellite as computed from the a-priori velocity vector of the carrier and from the data of the satellite, pvA being the pseudo-velocity between the carrier and the i-th satellite as measured by the GNSS receiver, and rpvi the variance of the pseudo-velocity measured pVi.

Within the context of the tight hybridization of Figure 3, the elements to be taken into consideration when defining the Kalman filter, apart from the matrix F reflecting the equation of change of the model are: for the part relating to the position readjustment : X- ΛΓ, α. = ■ pt ρ, = ^{χ~χ,Υ 5x,5y,6z being the deviations between the co-ordinates of the carrier's actual position and the co-ordinates of the carrier's position given by the navigation computer, t being the error made in the time by the clock of the GNSS receiver, which error is rendered akin to a distance by multiplying by the velocity of light, ai Pi'Yi being the direction cosines of the axis joining the carrier to the i-th satellite in the reference frame used by the navigation computer, x,y,z being the the co-ordinates of the carrier's position given by the navigation computer, xifYi'zi being the co-ordinates of the position of the i-th satellite of the positioning system as extracted from the data of the i-th satellite, and expressed in the reference frame used for the position of the carrier, Pi being the computed pseudo-distance between the carrier and the i-th satellite, pdA being the pseudo-distance between the carrier and the i-th satellite as measured by the GNSS receiver, and rpdi the variance of the pseudo-distance measured pdi. for the velocity readjustment part: dp, = (>', - .]cz, + (v - v„ )?, +(v, - )r, δ^,δ^,δ^ being the deviations between the components of the actual velocity vector of the carrier and those given by the navigation computer, d being the drift of the clock of the GNSS receiver, which drift is rendered akin to a velocity by multiplying by the velocity of light, vx'vy#vz being the carrier's velocity vector components given by the navigation computer, vxi,vyi,vzi being the components of the velocity vector of the i-th satellite of the positioning system extracted from the data of the i-th satellite itself, as expressed in the reference frame used by the navigation computer, dpi being the computed pseudo-velocity between the carrier and the i-th satellite, pVi being the pseudo-velocity between the carrier and the i-th satellite as measured by the GNSS receiver, and r i the variance of the pseudo-velocity measured pvi.

To improve the hybridization between an inertial rig and a GNSS receiver, a novel arrangement represented diagrammatically in Figure 4 is proposed.

As before, the inertial measurement unit I U 10 delivers increments of angles Δφχ,Δφν,Δφζ and increments of velocity Δνχ, AVy, Δνζ in a trihedral of orientation x, y, z tied to its sensors, to a navigation computer 11 responsible for extracting from these increments of angles and velocity, the position P, the velocity vector V and the attitudes Att of the carrier, whilst the GNSS receiver 13 supplies another version of the position P and the velocity vector V of the carrier.

Here, the GNSS receiver 13 is again regarded in its entirety, as in the case of loose hybridization, as having no direct access to the intermediate information delivered by its reception part, namely its measurements of pseudo-distances and of pseudo-velocities, thereby making it possible to avoid the problems connected with the output from its box of sensitive information. Only the final information is utilized, that is to say that pertaining to position, velocity vector, clock and the data transmitted by the satellites of the positioning system, which data are delivered by its computation part 13b.

As in the context of the loose hybridization described with reference to Figure 2, the deviations noted between the two versions of the carrier's position and velocity information originating on the one hand from the navigation computer 11 itself and on the other hand from the GNSS receiver are used for the correction of the errors of the navigation computer 11. However, instead of being used as they stand in the measurement vector of a Kalman filter delivering the presets for readjusting the navigation computer, as in the case of loose hybridization, the position deviation ΔΡ and velocity vector deviation Δν are transformed beforehand by a synthesizer circuit SA 30 into a pseudo-distance deviation Apd and pseudo-velocity deviation Δρν. This pseudo-distance deviation Apd and this pseudo-velocity deviation Δρν are then used, as in the context of the tight hybridization described with reference to Figure 3, as components of the measurement vector of the Kalman filter 32 delivering the presets for readjusting the navigation computer 11.

The synthesizer circuit SA receives the two versions of the position information P and velocity vector information V delivered the one by the navigation computer 11 and the other by the satellite-based positioning receiver 13 with, moreover, the positions Pi and velocity vectors VA of the visible satellites of the positioning system as extracted from the data transmitted by these satellites and picked up and decoded in the satellite-based positioning receiver 13.

To carry out the synthesis of the pseudo-distance deviations Apd and pseudo-velocity deviations Δρν using these basic items of information, one needs, at an intermediate stage, the direction cosines Oi,^i,yi of the satellite axes in the reference frame used by the navigation computer and the GNSS receiver.

For the determination of the direction cosines of the satellite axes, it makes use of the co-ordinates of the positions of the visible satellites of the positioning system and of the co-ordinates x,y,z of the position of the carrier. The co-ordinates of the positions χ-.±ιγί,ζί of the visible satellites are supplied to it by the GNSS receiver. For the co-ordinates x,y, z of the position of the carrier, it has the choice between two sources, either the GNSS receiver 13 or the navigation computer 11.

From these various co-ordinates, it implements the classical relations: p. = V(*-- 2 +(y- )2 +(' --,)2 and X-X. x. = P, It is advantageous for the synthesizer circuit SA 30 to use, during the determination of the direction cosines of the satellite axes, the information items relating to the co-ordinates x,y, z of the position of the carrier originating from the navigation computer 11, rather than those items originating from the GNSS receiver 13 since they are always available, thereby enabling the synthesizer circuit SA 30 to compute the direction cosines of the directions of all the visible satellites and therefore to arrive at the pseudo-distances and pseudo-velocities of these satellites, even if there is an insufficient number of them to enable the GNSS receiver to supply an estimation of the position of the carrier.

However, it is possible for the latter to use, during the determination of the direction cosines of the satellite axes, the information items relating to the co-ordinates x,y,z of the position of the carrier originating from the satellite-based positioning receiver. It is even possible for the direction cosines of the directions of the visible satellites to be supplied to it directly by the satellite-based positioning receiver since they do not form part of the sensitive information.

The Kalman filter 32 is similar to that (22 Figure 3) described in the context of "tight" hybridization, with the exception of the observation vector which has, as components: as regards the pseudo-distances, the quantities: with x y · position estimated by the navigation computer in z the terrestrial reference frame XGNSS >>GNSS position estimated by the GPS receiver in the ZGNSS . terrestrial reference frame (the diagonal term of the state noise matrix Q corresponding to the estimated clock bias is elevated, for example to a value greater than 106, so as not to take account of the time t estimated at the previous readjustment since we are no longer seeking to model the clock of the GNSS receiver in this kind of hybridization) and as regards the pseudo-velocities, the quantities: with velocity vector in the terrestrial reference delivered by the navigation computer vxGNSS vyGNSS velocity vector in the terrestrial reference fra by the GPS re vzGNSSJ me delivered ceiver (in the same way, the diagonal term of the state noise matrix Q corresponding to the estimated clock drift is also elevated, for example to a value greater than 106, so as not to take account of the drift d estimated at the previous readjustment since we are no longer seeking to model the clock of the GNSS receiver in this kind of hybridization) If the error t and the drift d of the clock of the GNSS receiver as estimated by its computation part are available at output, it is possible to take account thereof in the measurement vector: for the position readjustment a, (x - xGNSS)+ β. - yCNSS )+ ∑'*ONSs l Z = XGNSS)+ fit(y-yCNSS)+Y,(Z - ∑0NSS for the velocity readjustment - ) + βι ("v - V WB )+ *(v-- - In this case, it is advantageous to model the behaviour of the clock of the GNSS receiver in the equation of change .

The novel arrangement of hybridization between an inertial rig and a GNSS receiver as illustrated in Figure 4 has the aggregate advantages of tight hybridization and loose hybridization, when the information regarding the position and the velocity vector of the carrier as used by the synthesizing circuit for computing the direction cosines of the directions of the visible satellites originate from the navigation computer.

Specifically, as in tight hybridization, it makes it possible to take account, for the correction of the drift of the navigation computer, of the accuracy of the information delivered by the GNSS receiver, which accuracy is very dependent on the geometry of the constellation of satellites which it uses at the time of its triangulation (Dilution Of Precision) . It also allows some readjustment of the navigation computer as soon as at least one of the satellites of the positioning system is visible from the GNSS receiver, this readjustment improving with an increase in the number of satellites received (when the number of satellites available is less than four, the computer of the receiver supplies a partially readjusted position from an a-priori position, deduced for example from the previous solution) .

As in loose hybridization, it does not have recourse to any information which is confidential on the part of the GNSS receiver, the accuracy in the direction cosines of the satellite axes used by the circuit for synthesizing the pseudo-distance deviations and pseudo-velocity deviations not being critical.

To facilitate understanding, the navigation computer, the synthesizing circuit and the Kalman filter used for the correction of the errors of the inertial rig have been represented in the form of an assemblage of separate boxes. It should not be concluded therefrom that this is necessarily the case in practice. Indeed, since we are dealing with signals which are very often digitized, all the processing and functions carried out in these various boxes may so be by means of one or more processors driven by software and grouped together in the navigation computer.

Claims

1. CLAIMS Device for the hybridization, within a navigation computer (11) , of a satellite-based positioning receiver (13) with an inertial rig (10) equipping a craft, comprising a Kalman filter (32) , with an input and an output, based on the modelling of the dynamic behaviour of a system and defined by: a state vector with, among its components, the expected errors in the position co-ordinates, the components of the velocity vector, which are extracted from the acceleration components and from angular velocities delivered by the navigation computer, an equation of change reflecting the known laws of change of the components of its state vector, a measurement vector with, among its components, deviations between two versions of pseudo-distances and of pseudo-velocities having as origin the one the satellite-based positioning receiver and the other the navigation computer, an observation equation reflecting the dependency relations existing between the measurement vector and the state vector, characterized in that it comprises, interposed in front of the input of the Kalman filter, a synthesis circuit (30) for synthesizing the deviations between pseudo-distances and pseudo-velocities operating on the basis of the two versions of the craft's position and velocity vector information delivered, the one by the satellite-based positioning receiver (13) and the other by the navigation computer (11) and using, to do this, the direction cosines of the axes joining the craft to the visible satellites of the positioning system as deduced from the positions of the said visible satellites as derived from the data transmitted by them and picked up by the satellite-based positioning receiver (13) , and from one of the available versions of the craft's position information.

2. Device according to Claim 1, characterized in that the synthesis circuit (30) deduces the direction cosines of the axes joining the craft to the visible satellites of the positioning system, from the positions of the said visible satellites as extracted from the data transmitted by them and picked up by the satellite-based positioning receiver (13), and from the version of the craft's position information delivered by the navigation computer (11) .

3. Device according to Claim 1, characterized in that the synthesis circuit (30) deduces the direction cosines of the axes joining the craft to the visible satellites of the positioning system, from the positions of the said visible satellites as extracted from the data transmitted by them and picked up by the satellite-based positioning receiver (13), and from the version of the craft's position information delivered by the satellite-based positioning receiver (13) .

4. Device according to Claim 1, characterized in that the synthesis circuit (30) receives the values of the direction cosines of the axes joining the craft to the visible satellites of the positioning system directly from the satellite-based positioning receiver (13) which itself deduces them from the positions of the said visible satellites as extracted from the data transmitted by them and from its own version of information regarding the position of the craft.

5. Device according to Claim 1, character zed in that the Kalman filter has, among the components of its state vector, the bias and the drift of the clock of the receiver. .-or the ^Applicants